Abstract

For the purpose of studying those properties of a nonlinear function $f(u)$ for which the two-point boundary value problem $u''+\lambda f(u)=0 (0<x<1)$, $u'(0)=u(1)=0$ has a multiplicity of positive solutions for some $\lambda>0$, the authors construct a number of kinds of special examples. "Inverse" in the title refers to the fact that the multiplicity is specified first and then a suitable function $f$ is constructed.